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At least 19 recordsLinked to original sources
PubMed1998

Analyte-Receptor Binding Kinetics for Biosensor Applications: A Single-Fractal and a Dual-Fractal Analysis of the Influence of the Fractal Dimension on the Binding Rate Coefficient.

The diffusion-limited binding kinetics of antigen (analyte) in solution to antibody (receptor) immobilized on a biosensor surface is analyzed within a fractal framework. Most of the data presented are adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot ("Scientific Graphing Procedure, User's Manual," Jandel Scientific, San Rafael, CA, 1993). A couple of examples of a dual-fractal analysis are also presented. It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes in the same direction for the analyte-receptor systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the analyte-receptor binding systems indicate the high sensitivity of the binding rate coefficient on the fractal dimension when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis and for the binding of cell surface proteins from Helicobacter pylori strain in solution to sialyl-(alpha-2,3)-lactose-conjugated (20 mol%) polyacrylamide immobilized on a resonant mirror biosensor (S. Hirmo et al., Anal. Biochem. 257, 63, 1998), the order of dependence of the binding rate coefficient, k, on the fractal dimension, Df, was 14.15. The fractional order of dependence of the binding rate coefficient(s) on the fractal dimension(s) further reinforces the fractal nature of the system. The binding rate coefficient(s) expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface and further emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance. Copyright 1998 Academic Press.

Journal Article↗
PubMed1997

Characterisation of structural changes in the arterial elastic matrix by a new fractal feature: directional fractal curve.

A new fractal feature, the Directional Fractal Curve (DFC), defined over an arc of 180 and composed of 90 fractal dimensions determined at intervals of arc of 2, is developed to account for the anisotropic property of a fractal texture. The DFC algorithm is first applied to two images with different textural patterns, one without directional preference and one with a well-organised texture. The DFC of these images shows different patterns. The technique is then applied to quantify the structure of the elastic texture in the arterial wall where the elastic network was imaged by scanning electron microscopy following selective tissue digestion. The results suggest: (i) that images of the elastin matrix of the arterial wall exhibit fractal properties with directional preference, (ii) the DFC gives quantitative parameters which allow characterisation of structural changes in the elastin matrix of the arterial wall in terms of disorganisation and fragmentation of elastin fibres-conditions which are associated with medial degeneration due to normal ageing or presence of arterial disease.

Algorithms↗
PubMed1998

Neurons and fractals: how reliable and useful are calculations of fractal dimensions?

In the past 15 years it has become possible to determine the fractal dimension (Df) of complex objects, including neurons, by automated image analysis methods. However, there are many unresolved issues that need to be addressed. In this paper we discuss how the Df calculated by different methods may vary and how fractal analysis may be of use for retinal ganglion cell characterization. The goal of this work was to acknowledge inherent sources of variation during measurement and evaluate current fractal analysis methods for describing structure. Our results show that different algorithms and even the same algorithm performed by different computer programs and/or experimenters may give different but consistent numerical values. All described methods demonstrated their suitability for classifying cat retinal ganglion cells into distinct groups. Our results reinforce the idea that comparison of measurements of different profiles using the same measurement method may be useful and valid even if an exact numeric value of the dimension is not realised in practice.

Animals↗
PubMed1997

Estimating fractal dimension with fractal interpolation function models.

Fractal dimension (fd) is a feature which is widely used to characterize medical images. Previously, researchers have shown that fd separates important classes of images and provides distinctive information about texture. We analyze limitations of two principal methods of estimating fd: box-counting (BC) and power spectrum (PS). BC is ineffective when applied to data-limited, low-resolution images; PS is based on a fractional Brownian motion (fBm) model-a model which is not universally applicable. We also present background information on the use of fractal interpolation function (FIF) models to estimate fd of data which can be represented in the form of a function. We present a new method of estimating fd in which multiple FIF models are constructed. The mean of the fd's of the FIF models is taken as the estimate of the fd of the original data. The standard deviation of the fd's of the FIF models is used as a confidence measure of the estimate. We demonstrate how the new method can be used to characterize fractal texture of medical images. In a pilot study, we generated plots of curvature values around the perimeters of images of red blood cells from normal and sickle cell subjects. The new method showed improved separation of the image classes when compared to BC and PS methods.

Fractals↗
PubMed1994

Fractal analysis of pulmonary arteries: the fractal dimension is lower in pulmonary hypertension.

We analyzed the spatial structure of contact radiographs of barium-filled pulmonary arteries of rats raised in room air and in two environments that induce pulmonary arterial hypertension (PAH)--hypoxia and hyperoxia. We found that the spatial structure of the pulmonary arteries was fractal in both the control and the hypertensive lungs. The fractal dimension of the pulmonary arteries of the control lungs was 1.62 +/- 0.01 (mean +/- SEM), which is greater than that of both the hypoxic lungs 1.50 +/- 0.03 (p < 0.01) and the hyperoxic lungs 1.44 +/- 0.01 (p < 0.01). There was no significant difference between the hypoxic and hyperoxic lungs. The fractal dimension may be a useful clinical index to quantify pathologic changes in the pulmonary arterial tree.

Animals↗
PubMed1996

Fractal analysis of spinal dorsal horn neuron discharges by means of sequential fractal dimension D.

The present study describes a new method for converting a typical point process, such as a train of neuronal action potentials (spikes), into a planar curve which is then processed by means of a fast algorithm to calculate and display the fractal dimension D values of each of a sequence of blocks having an equal and preselectable number of interspike intervals, hence the term sequential fractal dimension D (SFD). This method is fast, does not require special computing facilities, and provides a continuous, high temporal resolution display of the neuronal discharge complexity along the course of spontaneous activity or event relating changes. The method affords insight into short duration changes in neuronal behaviour in a way independent of its discharge rate. SFD analysis of spike trains from spinal dorsal horn neurons suggests that the neuronal response to a given stimulus can be expressed as changes in the discharge pattern complexity, thus revealing a novel sensory coding strategy.

Action Potentials↗
PubMed1998

An analysis of analyte-receptor binding kinetics for biosensor applications: influence of the fractal dimension on the binding rate coefficient.

The diffusion-limited binding kinetics of analyte in solution to receptor immobilized on a biosensor surface is analysed within a fractal framework. Both a single- as well as a dual-fractal analysis are utilized. Antigen-antibody and analyte-receptor systems are analysed. For the antigen-antibody and analyte-receptor systems where a single- or a dual-fractal analysis was used, it is of interest to note that the binding rate coefficient and the fractal dimension exhibit changes in the same direction. The binding rate coefficient expressions obtained as a function of the fractal dimension indicate the high sensitivity of the binding rate coefficient with respect to the fractal dimension. For example, for a single-fractal analysis and for the binding of (a) 1 microM BSA in solution to the anti-BSA-protein fused to a biosensor surface, and for (b) the binding of m-xylene-saturated STE buffer solution to the microorganism immobilized to the fiber-optic end and covered with a polycarbonate membrane, the orders of dependence of the binding rate coefficient on the fractal dimension were 5.535 and 3.314, respectively. This emphasizes the importance of the degree of heterogeneity on the biosensor surface and its impact on the binding rate coefficient, k. This high sensitivity is also indicated for a dual-fractal analysis, at least for the binding rate coefficient, k2. For example, during regeneration runs and for the binding of polymerase chain-reaction amplified DNA in solution to DNA capture protein immobilized on a fiber-optic biosensor, the order of dependence of k2 on Df2 was 3.399. The fractional order of dependence of the binding rate coefficient(s) on the fractal dimension(s) further reinforces the fractal nature of the system. The binding rate coefficient expressions developed as a function of the fractal dimension for both single-fractal analysis and dual-fractal analysis systems are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface. Also, the importance of the nature of the surface on biosensor performance is emphasized in a quantitative sense.

Antigen-Antibody Reactions↗
PubMed1999

A single- and a dual-fractal analysis of antigen-antibody binding kinetics for different biosensor applications.

The diffusion-limited binding kinetics of antigen (or antibody) in solution to antibody (or antigen) immobilized on a biosensor surface is analyzed within a fractal framework. The data is adequately described by a single- or a dual-fractal analysis. Initially, the data was modelled by a single-fractal analysis. If an inadequate fit was obtained then a dual-fractal analysis was utilized. The regression analysis provided by Sigmaplot, 1993 (Scientific Graphing Software: User's Manual. Jandel Scientific, San Rafael, CA) was utilized to determine if a single-fractal analysis is sufficient, or a dual-fractal analysis is required. In general, it is of interest to note that the binding rate coefficient and the fractal dimension exhibit changes in the same direction (except for a single example) for the antigen-antibody systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the antigen-antibody binding systems indicate a high sensitivity of the binding rate coefficient on the fractal dimension when both a single -as well as a dual-fractal analysis is used. For example, for a single-fractal analysis and for the binding of human endothelin-1 (ET-1) antibody in solution to ET-1(15-21) x BSA (bovine serum albumin) immobilised on a surface plasmon resonance surface, the order of dependence of the binding rate coefficient, k on the fractal dimension, Df is 7.0945. Similarly, for a dual-fractal analysis and for the binding of parasite L. donovani diluted pooled sera in solution to fluorescein isothiocyanate-labeled anti-human immunoglobulin IgG immobilized on an optical fibre, the order of dependence of k1 and k2 on Df1 and Df2 were 6.8018 and -4.393, respectively. Binding rate coefficient expressions are also developed as a function of the analyte (antigen or antibody) concentration in solution. The binding rate coefficient expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface, and emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance.

Animals↗
PubMed1999

A Single and a Dual-Fractal Analysis of Analyte-Receptor Binding Kinetics for Surface Plasmon Resonance Biosensor Applications.

The diffusion-limited binding kinetics of analyte in solution to either a receptor immobilized on a surface or to a receptorless surface is analyzed within a fractal framework for a surface plasmon resonance biosensor. The data is adequately described by a single- or a dual-fractal analysis. Initially, the data was modeled by a single-fractal analysis. If an inadequate fit was obtained then a dual-fractal analysis was utilized. The regression analysis provided by Sigmaplot (32) was used to determine if a single fractal analysis is sufficient or if a dual-fractal analysis is required. In general, it is of interest to note that the binding rate coefficient and the fractal dimension exhibit changes in the same direction (except for a single example) for the analyte-receptor systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the analyte-receptor binding systems indicate, in general, the high sensitivity of the binding rate coefficient on the fractal dimension when both a single- and a dual-fractal analysis is used. For example, for a single-fractal analysis and for the binding of human endothelin-1 (ET-1) antibody in solution to ET-115-21.BSA immobilized on a surface plasmon resonance (SPR) surface (33), the order of dependence of the binding rate coefficient, k, on the fractal dimension, Df, is 6.4405. Similarly, for a dual-fractal analysis and for the binding of 10(-6) to 10(-4) M bSA in solution to a receptorless surface (direct binding to SPR surface) (41) the order of dependence of k1 and k2 on Df1 and Df2 were -2.356 and 6.241, respectively. Binding rate coefficient expressions are also developed as a function of the analyte concentration in solution. The binding rate coefficient expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control SPR biosensor performance by linking it to the degree of heterogeneity that exists on the SPR biosensor surface. Copyright 1999 Academic Press.

Journal Article↗